You are riding a roller coaster when a shoe falls off your foot. The function y=300−16t2 represents the height y (in feet) of the shoe t seconds after it falls off your foot. The shoe lands on the top of an 11-foot-tall building. After how many seconds does the shoe hit the building?

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MrRoyal MrRoyal · Answer 1 · 2020-11-11T02:22:02+01:00

Answer:

Time to land on 11ft is 4.25 seconds

Step-by-step explanation:

Given

[tex]y = 300 - 16t^2[/tex]

Required

Solve for t when height is 11ft

This implies that [tex]y = 11[/tex]

So: substitute 11 for y in [tex]y = 300 - 16t^2[/tex]

[tex]11 = 300 - 16t^2[/tex]

Collect Like Terms

[tex]16t^2 = 300 - 11[/tex]

[tex]16t^2 = 289[/tex]

Express both sides as squares

[tex]4^2 * t^2 = 17^2[/tex]

[tex](4t)^2 = 17^2[/tex]

Take square roots of both sides (ignore negative)

[tex]4t = 17[/tex]

Solve for t

[tex]t = \frac{17}{4}[/tex]

[tex]t = 4.25[/tex]

Hence, time to land on 11ft is 4.25 seconds